The Democratic primary is heating up in the race for a Kentucky U.S. Senate seat next year. Attorney General Jack Conway has announced his candidacy. He joins Lieutenant Governor Daniel Mongiardo and former U.S. Customs Agent Darlene Fitzgerald Price in the Democratic primary.But in a website video announcing his run, the 39-year-old Conway seemed to be looking ahead to a possible general election race against the 77-year-old Republican incumbent, Jim Bunning.“As I see the challenges facing our Commonwealth, near double-digit unemployment rates, high school dropout rates that lead the nation, exploding health care costs, and looming dangers abroad… Kentucky, now is the time for a new generation of leadership," says Conway in the video.Conway has been Kentucky’s Attorney General for a little over a year. He narrowly lost a bid to Congress in 2002.